Let
![f(x)](/media/m/3/f/4/3f40d68090aa4fb60a440be4675c7aca.png)
be a monic polynomial of degree
![1991](/media/m/a/7/5/a753ed02a7c68fa968ba9f1bca0cc528.png)
with integer coefficients. Define
![g(x) = f^2(x) - 9.](/media/m/9/1/a/91a3c3ba0d70a4e58b5a999457de917f.png)
Show that the number of distinct integer solutions of
![g(x) = 0](/media/m/7/a/1/7a1d77fd0add3f76d716412027030c82.png)
cannot exceed
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Let $f(x)$ be a monic polynomial of degree $1991$ with integer coefficients. Define $g(x) = f^2(x) - 9.$ Show that the number of distinct integer solutions of $g(x) = 0$ cannot exceed $1995.$